You should be able to buy the vehicle net of VAT from a UK dealer, you need to inform them beforehand. I think you pay the UK VAT to the dealer and when you provide proof of paying Irish VAT they refund you. Don't think you can claim the UK VAT back if you haven't informed the dealer you're exporting the vehicle.
As to whether you have to pay IE VAT or not - depends on whether it's a "new means of transport":
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SSE